College Algebra, 4th Edition

Cumulative Review Exercises (Chapters P–4)

1. 1. x-intercept: 0; y-intercepts: 0, 2; symmetric about y-axis

2. 3. Center: $(-1,2);$ radius: 5

   

3. 5. $(-\infty ,-3)\cup (2,\infty )$

4. 7. Start with $y=\sqrt{x},$ shift 1 unit left, stretch vertically by a factor of 3, and shift 2 units down.

   

5. 9.

   1. Yes, $f^{-1}(x)={\left({\displaystyle \frac{x-1}{2}}\right)}^{1/3}$

   2. No

   3. Yes, $f^{-1}(x)=e^x$

6. 11.

   1. $(x-1)(x-2)(x+3)=x^3-7x+6$

   2. $x^4-1$

7. 13.

   1. $\log \sqrt{xy}$

   2. $\text{ln }{\displaystyle \frac{x^3}{y^2}}$

8. 15.

   1. $\{3\}$

   2. $\{1,3\}$

   3. 3.77

9. 17.

   1. $1,1,1,-2,-2,3$

   2. At $x=1$ and $x=3,$ the graph crosses the x-axis. At $x=-2,$ the graph touches but does not cross the x-axis.

   3. $f(x)\to \infty$ as $x\to \infty ;f(x)\to \infty$ as $x\to -\infty$